Question

Jayden is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Jayden booked a total of 20 rooms which can accommodate 52 guests altogether. Determine the number of small rooms reserved and the number of large rooms reserved.

Answer 1

• 12 large rooms
• 8 small rooms

Explanation:

If all were small rooms, 40 guests could be accommodated. Each large room accommodates 1 more guest, so there must be 52 -40 = 12 large rooms. The remaining 20 -12 = 8 rooms are small rooms.

Jayden reserved 12 large and 8 small rooms.

__

If you can't think without an equation, let x represent the number of large rooms. Then the number of guests accommodated is ...

3x + 2(20-x) = 52

x + 40 = 52

x = 52 -40 = 12 . . . . . . .number of large rooms

(20-x) = 20-12 = 8 . . . . number of small rooms